REANALYSES OF ANOMALOUS GRAVITATIONAL MICROLENSING EVENTS IN THE OGLE-III EARLY WARNING SYSTEM DATABASE WITH COMBINED DATA

Light curves of gravitational microlensing events are characterized by a smooth, symmetric, and non-repeating shape (Paczyński 1986). However, they often exhibit deviations from the standard form. The causes of the deviations include the binarity of either lensing objects (binary-lens events: Mao & Paczyński 1991) or lensed source stars (binary-source events: Griest & Hu 1992). Deviations can also arise due to higher-order effects caused by the finite size of a source star (finite-source effect: Nemiroff & Wickramasinghe 1994) and the positional changes of the observer (parallax effect: Gould 1992), lens (lens-orbital effect: Albrow et al. 2000; Park et al. 2013), and source star (xallarap effect: Alcock et al. 2001) induced by the orbital motions of the observer (Earth), lens, and source star, respectively.

Analyzing anomalies in lensing light curves is important because it provides useful information about the lenses and lensed stars. By analyzing the light curve of a binary-lens event, one can obtain information about the mass ratio between the lens components. Analyzing the light curve of a binary-source event yields the flux ratio between the binary-source components. If finite-source and parallax effects are simultaneously detected, one can uniquely determine the physical parameters of the lens including the mass and distance to the lens (Gould 1992).

However, interpretation of anomalous lensing events is difficult due to various reasons. One important reason is the degeneracy problem where lensing solutions based on different interpretations result in a similar anomaly pattern. For example, it is known that binary-lens and binary-source solutions can often result in a similar anomaly pattern (Gaudi 1998). Even if an anomaly is identified to be caused by a binary lens, ${{\chi }^{2}}$ distributions in the space of the lensing parameters are usually complex due to the nonlinear dependence of lensing magnifications on the parameters and thus there often exist multiple local minima resulting in similar anomaly patterns.

For the correct interpretation of lensing event by resolving the degeneracy problem, dense and continuous coverage of lensing light curves is important. Good coverage data are also important in extracting extra information about lenses and lensed stars by detecting subtle deviations caused by higher-order effects. In order to obtain correct interpretations of events and maximize information about lens systems, therefore, it is important to test all possible causes of anomalies based on all available data.

In a series of papers (Jaroszyński et al. 2006, 2010; Skowron et al. 2007), the Optical Gravitational Lensing Experiment (OGLE: Udalski 2003) group published lists of anomalous lensing events in the OGLE-III Early Warning System (EWS) database that is collected from the lensing survey conducted during the 2004–2008 period (hereafter the "OGLE Anomaly Catalog"). They also presented solutions of the anomalous events based on binary-lens and binary-source interpretations.

In this work, we reanalyze the anomalous events in the OGLE Anomaly Catalog. We conduct a thorough search for local solutions in order to investigate possible degeneracy. For analyses based on better coverage of anomalies, we include additional data obtained from other survey and follow-up observations. In addition, we consider higher-order effects that were not considered in the previous analyses.

Among the total of 68 events in the OGLE Anomaly Catalog, we conduct reanalyses of events for which the anomalies and overall light curves are well covered either by the OGLE data alone or with the addition of data from other survey and follow-up observations. Among the analyzed events, we present the results of eight events for which either new solutions are identified (five events) or additional information, such as the Einstein radius (three events) or the lens parallax (one event), is obtained.

Table 1 shows the list of events analyzed in this work along with their equatorial and ecliptic coordinates. Table 2 shows the data sets used in our analyses and the telescopes used for observation. Except for the event OGLE-2007-BLG-491, we use extra data in addition to the data from the OGLE survey. These additional data were taken from the survey conducted by the Microlensing Observations in Astrophysics (MOA: Bond et al. 2001; Sumi et al. 2003) group and the follow-up observation conducted by the Microlensing Follow-up Network (μFUN: Gould et al. 2006), Probing Lensing Anomalies NETwork (PLANET: Beaulieu et al. 2006), and RoboNet (Tsapras et al. 2009). We note that the OGLE data used in the OGLE Anomaly Catalog were based on the online data processed by automatic pipeline. In this work, we used new sets of data prepared by re-reducing the data that is optimized for individual events.

Table 1.  Events and Coordinates

Event	R.A. (J2000)	Decl. (J2000)	λ	β
OGLE-2006-BLG-215	17h59m0663	−29°08'55 7	26980	−571
OGLE-2006-BLG-238/MOA-2006-BLG-26	17h57m1166	−30°48'06 0	26939	−736
OGLE-2006-BLG-450	17h52m0047	−31°07'36 3	26827	−770
OGLE-2007-BLG-159	17h54m4168	−29°25'39 5	26884	−599
OGLE-2007-BLG-491	17h56m2868	−32°13'15 3	26925	−878
OGLE-2008-BLG-143/MOA-2008-BLG-111	17h59m3858	−28°41'34 8	26992	−525
OGLE-2008-BLG-210/MOA-2008-BLG-177	17h59m2297	−27°42'30 2	26986	−427
OGLE-2008-BLG-513/MOA-2008-BLG-401	17h52m4351	−30°51'33 2	26843	−743

Download table as:  ASCIITypeset image

In Figures 1 through 8, we present the light curves of the events. Also presented are the best-fit models obtained from our analyses and the residuals from the models. For the case where new solutions are identified, we present two panels of residuals from the new and previous solutions. See more details in Section 4.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

Data sets used for the analyses were processed using the photometry codes developed by the individual groups. Since the individual data sets were obtained using different telescopes, it is necessary to readjust their error bars. The error bars of each data set are adjusted by

$$\begin{eqnarray}&&e^{\prime} =k{{\left( {{e}^{2}}+{{e}_{{\rm min} }} \right)}^{1/2}}.\end{eqnarray} \tag{ 1 }$$

Here ${{e}_{{\rm min} }}$ is a term introduced so that the cumulative distribution function of ${{\chi }^{2}}$ as a function of lensing magnification becomes linear. This factor is needed to ensure that the dispersion of data points is consistent with the error bars of the source brightness. The other term k is a scaling factor used to make ${{\chi }^{2}}$ per degree of freedom (dof) unity. This process is needed to ensure that each data set is fairly weighted according to its error bars.

Light curves of binary-lens events are generally characterized by distinct sharp spikes occurring at the moments of caustic crossings. For events with such features (OGLE-2006-BLG-215, OGLE-2006-BLG-238, OGLE-2006-BLG-450, and OGLE-2008-BLG-513), we conduct binary-lens analyses. On the other hand, light curves of binary-lens events without caustic crossings do not exhibit such features and the resulting anomalies can often be imitated by those of binary-source events. For such events (OGLE-2007-BLG-159, OGLE-2007-BLG-491, OGLE-2008-BLG-143, and OGLE-2008-BLG-210), we conduct both binary-source and binary-lens analyses.

In the analyses, we consider higher-order effects. The first such effect is caused by the finite size of the source star. For binary-lens events, this effect is important for caustic-crossing parts of the light curve where lensing magnifications vary abruptly with a small change of the source position and thus differential magnification on the surface of the source star becomes important. Among the analyzed binary-lens events, caustic crossings were resolved by the OGLE data for only one event (OGLE-2006-BLG-215), while caustics were resolved with combined data for all caustic-crossing events. We also consider the effects caused by the parallactic motion of the Earth and the orbital motion of lenses. These effects are important for long timescale events where the duration of the event is equivalent to the orbital period of the Earth and lenses.

Modeling lensing events requires parameters that describe observed light curves. The light curve of a single-lens event is described by three parameters. They are the time of the closest approach of the source to the reference position of the lens, t₀, the lens–source separation at that moment, u₀ (impact parameter), and the event timescale, ${{t}_{{\rm E}}}$, which is defined as the time for the source to cross the Einstein radius of the lens. The Einstein radius is related to the physical parameters of the lens system by

$$\begin{eqnarray}&&{{\theta }_{{\rm E}}}={{\left( \kappa M{{\pi }_{{\rm rel}}} \right)}^{1/2}};{{\pi }_{{\rm rel}}}={\rm AU}\left( \frac{1}{{{D}_{{\rm L}}}}-\frac{1}{{{D}_{{\rm S}}}} \right),\end{eqnarray} \tag{ 2 }$$

where $\kappa =4\;G/\left( {{c}^{2}}{\rm AU} \right)$, M is the total mass of the lens, ${{\pi }_{{\rm rel}}}$ is the relative source-lens parallax, and ${{D}_{{\rm L}}}$ and ${{D}_{{\rm S}}}$ are the distances to the lens and source, respectively. The Einstein radius is used as a length scale in describing lensing phenomenon and u₀ is normalized by ${{\theta }_{{\rm E}}}$.

The light curve of a binary-source event corresponds to the linear sum of the fluxes from the two single-source events involved with the individual source stars. Then, describing the light curve requires two values of t₀ (${{t}_{0,1}}$ and ${{t}_{0,2}}$) and u₀ (${{u}_{0,1}}$ and ${{u}_{0,2}}$) but a single timescale because it is related only to the lens. One additional parameter is the flux ratio ${{q}_{{\rm F}}}$ between the source components.

In order to model a binary-lens event, additional parameters are needed to describe the lens binarity. They are the projected separation s and the mass ratio q between the lens components. We note that the separation is normalized by ${{\theta }_{{\rm E}}}$. Due to the lens binarity, positions around the lens are no longer radially symmetric. Then, one needs an additional parameter α designating the angle between the source trajectory and the line connecting the binary lens components (source trajectory angle).

In order to consider higher-order effects, one also needs additional parameters. Accounting for finite-source effects requires a parameter defined as the angular source radius ${{\theta }_{\star }}$ expressed in units of the Einstein radius ${{\theta }_{{\rm E}}}$, $\rho ={{\theta }_{\star }}/{{\theta }_{{\rm E}}}$ (normalized source radius). Considering parallax effects requires two parameters ${{\pi }_{{\rm E},N}}$ and ${{\pi }_{{\rm E},E}}$ that are the north and east components of the lens parallax vector, ${{{\boldsymbol{ \pi }} }_{{\rm E}}}$, projected on the sky in the north and east equatorial coordinates, respectively. The lens parallax vector is defined as

$$\begin{eqnarray}&&{{{\boldsymbol{ \pi }} }_{{\rm E}}}=\frac{{{\pi }_{{\rm rel}}}}{{{\theta }_{{\rm E}}}}\frac{{\boldsymbol{ \mu }} }{\mu },\end{eqnarray} \tag{ 3 }$$

where ${\boldsymbol{ \mu }}$ represents the vector of the relative lens–source proper motion. In order to account for lens-orbital effects, one needs two parameters including the change rates of the projected binary separation, $ds/dt$, and the source trajectory angle, $d\alpha /dt$. When either the parallax or the lens-orbital effects are considered, we test two solutions with the lens–source impact parameters ${{u}_{0}}\gt 0$ and ${{u}_{0}}\lt 0$ in order to check the known "ecliptic degeneracy" (Skowron et al. 2011).

In our analysis, we search for the set of the lensing parameters that best describes the observed light curves. For binary-source modeling where lensing magnifications vary smoothly with the parameters, searching for lensing solutions is done by minimizing ${{\chi }^{2}}$ using a downhill approach. For the downhill approach, we use the Markov Chain Monte Carlo method. For binary-lens modeling, on the other hand, the search is done through multiple steps. In the first step, we inspect local minima by exploring ${{\chi }^{2}}$ surface in the parameter space. For this, we conduct a grid search for a subset of the lensing parameters. We choose $(s,q,\alpha )$ as grid parameters because lensing magnifications can vary dramatically with small changes of these parameters. On the other hand, lensing magnifications vary smoothly with the changes of the other parameters and thus we search for these parameters by using a downhill approach. In the second step, we refine each local minimum by letting all lensing parameters vary around the minimum. In the final step, we find the global minimum by comparing the ${{\chi }^{2}}$ values of the identified local minima. This multiple-step process allows one to check the existence of possible degenerate solutions that cause confusion in the interpretation of the observed light curves.

In computing finite-source magnifications, we consider the limb-darkening variation of source stars. For this, we model the surface brightness profile of the source star as

$$\begin{eqnarray}&&{{S}_{\lambda }}\propto 1-{{{\Gamma }}_{\lambda }}(1-1.5{\rm cos} \psi ),\end{eqnarray} \tag{ 4 }$$

where ${{{\Gamma }}_{\lambda }}$ is the limb-darkening coefficient and ψ is the angle between the line of sight toward the source center and the normal to the source surface. We adopt the limb-darkening coefficients from Claret (2000) based on the source types that are determined from the de-reddened color and brightness of the source stars measured by using the multi-band (V and I) data taken from CTIO observation. Among the six caustic-crossing events, there exist multi-band data for three events and thus the source types are able to be determined. For OGLE-2006-BLG-215 and OGLE-2006-BLG-450, which were observed in I band only, we adopt ${{{\Gamma }}_{I}}=0.5$ by taking the median value of bulge stars.

In Table 3, we present the best-fit lensing parameters obtained from modeling. In order to present lensing parameters of all events in a single table, we do not present the value of t₀ that has no physical meaning in describing a lens system. It is found that all eight analyzed events are interpreted to be caused by binary lenses. The model light curves corresponding to the best-fit solutions of the individual events are superposed on the light curves in Figures 1 through 8.

Table 3.  Binary Lens Parameters of Newly Analyzed Events

Event	Solution	${{\chi }^{2}}/{\rm dof}$	u0	${{t}_{{\rm E}}}$	s	q	α	ρ	${{\pi }_{{\rm E},N}}$	${{\pi }_{{\rm E},E}}$
				(days)			(rad)	$({{10}^{-3}})$
OGLE-2006-BLG-215		1628.3	0.468	27.4	1.01	1.09	5.828	9.07	⋯	⋯
		/1552	±0.008	±0.4	±0.01	±0.05	±0.009	±0.21	⋯	⋯
OGLE-2006-BLG-238/	$s\lt 1$	2177.6	0.079	14.9	0.90	0.08	1.687	1.86	⋯	⋯
MOA-2006-BLG-26		/2151	±0.008	±0.8	±0.01	±0.01	±0.023	±0.26	⋯	⋯
	$s\gt 1$	2163.7	0.068	15.3	1.33	0.12	1.651	2.44	⋯	⋯
		/2151	±0.008	±0.8	±0.02	±0.01	±0.010	±0.35	⋯	⋯
OGLE-2006-BLG-450		1008.8	0.139	8.6	0.90	0.59	1.258	10.31	⋯	⋯
		/1007	±0.012	±0.2	±0.01	±0.03	±0.021	±0.41	⋯	⋯
OGLE-2007-BLG-159		1634.7	0.684	18.0	1.10	1.61	−0.331	⋯	⋯	⋯
		/1639	±0.008	±0.2	±0.01	±0.05	±0.004	⋯	⋯	⋯
OGLE-2007-BLG-491	$s\lt 1$	910.2	0.244	32.1	0.61	0.35	3.774	⋯	⋯	⋯
		/904	±0.035	±3.2	±0.03	±0.08	±0.073	⋯	⋯	⋯
	$s\gt 1$	907.0	0.090	61.0	3.04	1.15	3.483	⋯	⋯	⋯
		/904	±0.019	±5.6	±0.35	±0.35	±0.053	⋯	⋯	⋯
OGLE-2008-BLG-143/	${{u}_{0}}\gt 0$	4598.8	0.191	62.9	2.62	1.17	2.566	15.34	0.19	0.16
MOA-2008-BLG-111		/4786	±0.002	±0.4	±0.02	±0.05	±0.005	±1.16	±0.01	±0.01
	${{u}_{0}}\lt 0$	4606.9	−0.202	60.5	2.70	1.31	−2.578	16.11	−0.12	0.18
		/4786	±0.002	±0.5	±0.02	±0.04	±0.005	±1.65	±0.01	±0.02
OGLE-2008-BLG-210/		3436.2	0.027	19.3	0.22	1.04	5.265	12.32	⋯	⋯
MOA-2008-BLG-177		/3480	±0.001	±0.2	±0.01	±0.05	±0.006	±0.24	⋯	⋯
OGLE-2008-BLG-513/		4951.7	0.079	35.4	0.91	0.30	5.590	2.38	⋯	⋯
MOA-2008-BLG-401		/4972	±0.001	±0.5	±0.01	±0.01	±0.003	±0.03	⋯	⋯

Note. For OGLE-2008-BLG-143, two solutions resulting from the ecliptic degeneracy (with ${{u}_{0}}\gt 0$ and ${{u}_{0}}\lt 0$) are presented. For each of OGLE-2006-BLG-238, OGLE-2007-BLG-491, and OGLE-2008-BLG-210, two solutions resulting from the close/wide degeneracy (with $s\lt 1$ and $s\gt 1$) are presented.

Download table as:  ASCIITypeset image

We find that the previous binary-source interpretations of five events are better interpreted by binary-lens models. These events include OGLE-2006-BLG-238, OGLE-2007-BLG-159, OGLE-2007-BLG-491, OGLE-2008-BLG-143, and OGLE-2008-BLG-210.

With additional data covering caustic crossings, we additionally detect finite-source effects for six events. These events include OGLE-2006-BLG-215, OGLE-2006-BLG-238, OGLE-2006-BLG-450, OGLE-2008-BLG-143, OGLE-2008-BLG-210, and OGLE-2008-BLG-513. Among them, we are able to measure the Einstein radii of three events for which multi-band data are available and thus source types are known from color information. These events are OGLE-2006-BLG-238, OGLE-2008-BLG-210, and OGLE-2008-BLG-513. The Einstein radius is measured by ${{\theta }_{{\rm E}}}={{\theta }_{\star }}/\rho$, where the angular source radius ${{\theta }_{\star }}$ is estimated from the de-reddened color and brightness of the source star and the normalized source radius ρ is measured from modeling the light curve. The source radius is determined following the method of Yoo et al. (2004), where we first locate the source star on the color–magnitude diagram of stars in the field and then calibrate the de-reddened color and brightness of the source star by using the centroid of the red clump giants as a reference under the assumption that the source and red clump giants experience the same amount of extinction and reddening.

From the inspection of additional higher-order effects, we detect a clear signature of parallax effects for OGLE-2008-BLG-143. For OGLE-2006-BLG-215, we initially detect both parallax and lens-orbital effects from the analysis based on the online data, but find that the signals of these higher-order effects are spurious based on the analysis of the re-reduced data.

Finally, we identify additional solutions caused by the known degeneracy for three events. For OGLE-2006-BLG-238 and OGLE-2007-BLG-491, we identify degenerate solutions caused by the "close/wide" degeneracy. This degeneracy is caused by the symmetry of the lens-mapping equations between the binary lenses with separations s and ${{s}^{-1}}$ (Griest & Safizadeh 1998; Dominik 1999; An 2005). For OGLE-2008-BLG-143, we identify degenerate solutions caused by the ecliptic degeneracy. This degeneracy is caused by the mirror symmetry between the source trajectories with ${{u}_{0}}\gt 0$ and ${{u}_{0}}\lt 0$ with respect to the binary axis.

Below we describe details of the results from our analyses of the individual events. We then compare the results with those from the previous analyses.

4.1. OGLE-2006-BLG-215

4.2. OGLE-2006-BLG-238

In addition to the OGLE group, the event was observed by many other groups and the MOA group designated the event MOA-2006-BLG-26. In the OGLE Anomaly Catalog, this event was interpreted as a binary-source event. With the addition of follow-up data, especially the SAAO data set covering the caustic exit, it is clear that the event was produced by a binary lens. We find that a binary-lens interpretation is better than the binary-source interpretation by ${\Delta }{{\chi }^{2}}=5233.4$. See the residuals from the binary-lens and binary-source models presented in the lower two panels of Figure 2. From modeling the light curve including additional follow-up data, it is found that the event was produced by the source crossings over the single big caustic of a resonant binary. See Figure 9 for the source trajectory with respect to the caustic.

Zoom In Zoom Out Reset image size

With the coverage of the caustic crossing by the SAAO data and multi-band data obtained from CTIO observation, we measure the Einstein radius of the lens system. The measured de-reddened color and brightness of the source stars are ${{(}_{V-I,I)0}}=(1.24,17.7)$, which correspond to a K-type Bulge subgiant with ${{\theta }_{\star }}=1.66\pm 0.14$ μas. With the measured normalized source radius $\rho =(2.44\pm 0.35)\times {{10}^{-3}},$ then, the Einstein radius is ${{\theta }_{{\rm E}}}=0.68\pm 0.12$ mas.

We find that there exist two local solutions resulting from the close/wide degeneracy. The degeneracy is quite severe and the wide-binary solution $(s\gt 1)$ is preferred over the close-binary solution $(s\lt 1)$ by merely ${\Delta }{{\chi }^{2}}=13.9$. We present the lensing parameters of both close and wide binary solutions and the corresponding lens-system geometry in Table 3 and Figure 9, respectively. Due to the short timescale of the event, ${{t}_{{\rm E}}}\sim 15.3$ days, neither parallax nor lens-orbital effect is measured.

4.3. OGLE-2006-BLG-450

4.4. OGLE-2007-BLG-159

4.5. OGLE-2007-BLG-491

4.6. OGLE-2008-BLG-143

4.7. OGLE-2008-BLG-210

4.8. OGLE-2008-BLG-513

4.9. Physical Lens Parameters

Among the analyzed events, there is no event for which both the Einstein radius and the lens parallax are simultaneously measured and thus the mass and distance to the lens are uniquely measured. Nevertheless, it is still possible to constrain the physical lens parameters based on the event timescale. For events where either the Einstein radius or the lens parallax is additionally measured, the physical parameters can be better constrained.

To estimate the ranges of the mass and distance to each lens, we conduct Bayesian analysis based on the mass function, and spatial and velocity distributions of Galactic stars (Han & Gould 1995). In Table 4, we present the estimated ranges of the physical lens parameters. Note that the masses of the binary companions of the lens for the events OGLE-2006-BLG-450, OGLE-2008-BLG-210 are in the brown-dwarf regime. For OGLE-2007-BLG-159, the companion mass is at the star/brown-dwarf boundary.

Table 4.  Ranges of the Lens Mass and Distance

Event	Mass (${{M}_{\odot }}$)		Distance
	Primary	Companion	(kpc)
OGLE-2006-BLG-215	0.38 ± 0.23	0.11 ± 0.07	6.36 ± 1.52
OGLE-2006-BLG-238/MOA-2006-BLG-26	0.41 ± 0.22	0.11 ± 0.06	4.81 ± 1.09
OGLE-2006-BLG-450	0.19 ± 0.13	0.03 ± 0.02	7.28 ± 1.25
OGLE-2007-BLG-159	0.29 ± 0.19	0.07 ± 0.05	6.71 ± 1.40
OGLE-2007-BLG-491	0.49 ± 0.28	0.18 ± 0.10	5.63 ± 1.98
OGLE-2008-BLG-143/MOA-2008-BLG-111	0.36 ± 0.19	0.30 ± 0.16	6.78 ± 0.90
OGLE-2008-BLG-210/MOA-2008-BLG-177	0.26 ± 0.17	0.05 ± 0.04	7.35 ± 0.93
OGLE-2008-BLG-513/MOA-2008-BLG-401	0.45 ± 0.19	0.10 ± 0.04	6.98 ± 0.93

Download table as:  ASCIITypeset image

We reanalyzed anomalous lensing events in the OGLE-III EWS database. With the addition of data from other survey and follow-up observations, we conducted a thorough search for possible degenerate solutions and investigated higher-order effects. Among the analyzed events, we presented analyses of eight events for which either new solutions were identified by resolving the degeneracy in lensing solutions or additional information was obtained by detecting higher-order effects. We found that the previous binary-source interpretations of five events (OGLE-2006-BLG-238, OGLE-2007-BLG-159, OGLE-2007-BLG-491, OGLE-2008-BLG-143, and OGLE-2008-BLG-210) were better interpreted by binary-lens models. In addition, we detected finite-source effects for six events (OGLE-2006-BLG-215, OGLE-2006-BLG-238, OGLE-2006-BLG-450, OGLE-2008-BLG-143, OGLE-2008-BLG-210, and OGLE-2008-BLG-513) with additional data covering caustic crossings and measure the Einstein radii for three events (OGLE-2006-BLG-238, OGLE-2008-BLG-210, and OGLE-2008-BLG-513). For OGLE-2008-BLG-143, we detect a clear signature of parallax effects and measure the lens parallax. In addition, we presented degenerate solutions resulting from the known close/wide or ecliptic degeneracy. Finally, we note that the masses of the binary companions of the lenses of OGLE-2006-BLG-450 and OGLE-2008-BLG-210 are likely in the brown-dwarf regime according to the mass ranges estimated by Bayesian analysis.

Work by C.H. was supported by the Creative Research Initiative Program (2009-0081561) of the National Research Foundation of Korea. The OGLE project has received funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement no. 246678 to AU. The MOA project is supported by the grants JSPS18253002 and JSPS20340052. T.S. acknowledges the financial support from the JSPS, JSPS23340044 and JSPS24253004. D.P.B. was supported by grants NASA-NNX12AF54G, JPL-RSA 1453175, and NSF AST-1211875. B.S.G. and A.G. were supported by NSF grant AST 110347. B.S.G., A.G., and R.P.G. were supported by NASA grant NNX12AB99G. Work by J.C.Y. was performed in part under contract with the California Institute of Technology (Caltech) funded by NASA through the Sagan Fellowship Program.